TEMPUR SEALY INTERNATIONAL, INC. 2013 EQUITY INCENTIVE PLAN LONG-TERM INCENTIVE PLAN 2015 Performance Restricted Stock Unit Award Agreement Scott Thompson

Exhibit 10.5

TEMPUR SEALY INTERNATIONAL, INC.

2013 EQUITY INCENTIVE PLAN

LONG-TERM INCENTIVE PLAN

2015 Performance Restricted Stock Unit Award Agreement

Scott Thompson

This 2015 Performance Restricted Stock Unit Award Agreement (this “Agreement”), dated as of September 4, 2015, is between Tempur Sealy International, Inc., a corporation organized under the laws of the State of Delaware (the “Company”), and the individual identified below (the “Grantee”).

1. Award of Performance Restricted Stock Units. Pursuant and subject to the Company’s 2013 Equity Incentive Plan, as amended (as the same may be amended from time to time, the “2013 EIP”) and the Company’s 2013 Long-Term Incentive Plan as adopted in connection with the 2013 EIP (the “LTI Plan”), the Company grants the Grantee an award (the “Award”) for 620,000 performance restricted stock units (the “PRSUs”), each constituting the right on the terms and conditions set forth herein to a share of the Company’s common stock, par value $0.01 per share (the “Target Shares”) (as defined in Section 3 below). This Award is granted as of September 4, 2015 (the “Grant Date”) and is intended to qualify as a Qualified Performance-Based Award.

2. Rights of the PRSUs and Target Shares. The Grantee will receive no dividend equivalent payments on the PRSUs or with respect to the Target Shares. Unless and until a Final Award has been determined and the Grantee has received Target Shares in accordance with the terms and conditions described herein, the Grantee shall have none of the attributes of ownership with respect to any Target Shares.

3. Determination of Final Award

(a) The Target Shares ultimately issued by the Company pursuant to the Award shall be subject to the Company’s achievement (“Performance”) of the Performance Metrics for the Award and compliance with the provisions and rules set forth on Appendix A attached hereto (the “Performance Metrics”) and incorporated herein by this reference. Any determination that Target Shares have been earned with respect to the First Designated Period or the Second Designated Period as described below is

sometimes referred to as the “Final Award” with respect to such Designated Period, and the Target Shares to be issued with respect to such Designated Period are sometimes referred to as the “Shares”.

(b) As provided in the LTI Plan, within sixty (60) days after the end of the First Designated Period, the Compensation Committee of the Board of Directors (the “Committee”) shall determine and certify in writing (y) whether the Performance Metrics for the First Designated Period have been achieved and (z) based on such Performance, whether or not 100% of the Target Shares will be issued to Grantee (with the date of such determination referred to as the “First Determination Date”). Not later than March 15, 2018, if the Company achieved the Performance Metrics for the First Designated Period, the Company shall issue all of the Target Shares, to Grantee, subject to Section 7 of this Agreement relating to tax withholding (the date of such issuance being referred to herein as the “First Settlement Date”).

(c) If the Company achieves the Performance Metrics for the First Designated Period, then this paragraph (c) does not apply. If the Company does not achieve the Performance Metrics for the First Designated Period, then any right to 2/3 of the Target Shares (413,333 Target Shares) will be forfeited, but the Grantee will still be entitled to earn 1/3 of the Target Shares (206,667 Target Shares) if the Performance Metrics for the Second Designated Period are met. As provided in the LTI Plan, within sixty (60) days after the end of the Second Designated Period, the Committee shall determine and certify in writing (y) whether the Performance Metrics for the Second Designated Period have been achieved and (z) based on such Performance, whether or not 206,667 Target Shares will be issued to Grantee (with the date of such determination referred to as the “Second Determination Date” and together with the First Determination as “Determination Dates”). No later than March 15, 2019, if the Company did not meet the Performance Metrics for the First Designated Period but met the Performance Metrics for the Second Designated Period, the Company shall issue 206,667 Shares to Grantee, subject to Section 7 of this Agreement relating to tax withholding (the date of such issuance being referred to herein as the “Second Settlement Date” and together with the First Settlement Date as “Settlement Dates”). If the Company does not achieve the Performance Metrics for the Second Designated Period then all the remaining Target Shares will be forfeited, and this Agreement will terminate.

4. Termination of Employment.

(a) If the Grantee’s employment with the Company and its Affiliates terminates before December 31, 2017 for any reason, including because the Grantee’s employer ceases to be an Affiliate, the Grantee’s rights to the Target Shares shall terminate immediately, no Shares shall be issued to Grantee and all of the Grantee’s rights to the Target Shares and any Final Award hereunder shall be forfeited. In addition, notwithstanding anything herein to the contrary, if the Grantee’s employment terminates on or after December 31, 2017 and prior to the First Settlement Date, no Shares shall be issued with respect to the First Designated Period and all of the Grantee’s rights to any Final Award and any Target Shares otherwise due shall be forfeited, expire and terminate unless (i) the Company shall have received a release of all claims from Grantee in the form required by the Employment Agreement (“Release and Waiver”) (and said Release and Waiver shall have become irrevocable in accordance with its terms) prior to the First Settlement Date (or, if earlier, the deadline established in the form of release delivered by the Company to the Grantee for execution); (ii) the Grantee has ensured that the Company has a valid address for Grantee on file as of the end of the First Settlement Date; and (iii) the Grantee shall have complied with the covenants set forth in Section 12 of this Agreement.

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(b) If the Grantee’s employment with the Company and its Affiliates terminates on or after December 31, 2017 but before December 31, 2018 for any reason, including because the Grantee’s employer ceases to be an Affiliate, the Grantee’s rights to the Target Shares issuable with respect to the Second Designated Period shall terminate immediately, no Shares shall be issued to Grantee and all of the Grantee’s rights to the Target Shares and any Final Award hereunder with respect to the Second Designated Period shall be forfeited. In addition, notwithstanding anything herein to the contrary, if the Grantee’s employment terminates on or after December 31, 2018 and prior to the Second Settlement Date, no Shares shall be issued with respect to the Second Designated Period and all of the Grantee’s rights to any Final Award and any Target Shares otherwise due shall be forfeited, expire and terminate unless (i) the Company shall have received a Release and Waiver from Grantee (and said Release and Waiver shall have become irrevocable in accordance with its terms) prior to the Second Settlement Date (or, if earlier, the deadline established in the form of release delivered by the Company to the Grantee for execution); (ii) the Grantee has ensured that the Company has a valid address for Grantee on file as of the end of the Second Settlement Date; and (iii) the Grantee shall have complied with the covenants set forth in Section 12 of this Agreement.

(c) Definitions. For the purposes of this Agreement:

(i) “Change of Control” shall have the meaning set forth in the Plan, provided, that no event or transaction shall constitute a Change of Control for purposes of this Agreement unless it also qualifies as a change of control for purposes of Section 409A of the Code;

(ii) “Employee”, “employment”, “termination of employment” and “cease to be employed”, and other words or phrases of similar import, shall mean the continued provision of substantial services to the Company or any of its Affiliates (or the cessation or termination of such services) whether as an employee, consultant or director;

(iii) “Employment Agreement” shall mean the Employment Agreement, dated as of September 4, 2015 between the Company and the Grantee.

(iv) “For Cause” shall have the meaning set forth in the Employment Agreement.

(v) “Good Reason” shall have the meaning set forth in the Employment Agreement.

(vi) “Retirement” shall have the meaning assigned to such term in the applicable retirement policy of the Company or its Affiliates as in effect at such time.

5. Change of Control Provisions. Pursuant to Section 9 of the 2013 EIP and subject to paragraph (b) below, immediately upon the occurrence of a Change of Control, all of the PRSUs subject to this Award that have not already become payable pursuant to Section 3(b) or Section 3(c) and that not have already been forfeited (“Outstanding Unvested PRSUs”) shall convert to time-based vesting restricted stock units (“RSUs”, with the shares of the Company’s common stock issuable thereunder referred to as “RSU Shares”), without any pro-ration, as follows:

(a) the Grantee shall be entitled to receive RSUs equal to the number of Outstanding Unvested PRSUs in lieu of any claim to a Final Award.

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(b) if the Change of Control occurs on or after December 31, 2017 but before the determination of whether the Performance Metrics for the First Designated Period have been met, (i) if the Performance Metrics for the First Designated Period are determined to have been met in accordance with Section 3 and Appendix A, the Outstanding Unvested PRSUs shall become payable in accordance with Section 3(b) and no Outstanding Unvested PRSUs shall convert into RSUs as described above, and (ii) if it is determined that the Performance Metrics for the First Designated Period were not met, then 2/3 (or 413,333) of such Outstanding Unvested PRSUs shall terminate and be forfeited as provided in Section 3(c) and 1/3 (or 206,667) RSUs will be issued.

(c) if the Change of Control occurs on or after December 31, 2018 but before the determination of whether the Performance Metrics for the Second Designated Period have been met, (i) if the Performance Metrics for the Second Designated Period are determined to have been met in accordance with Section 3 and Appendix A, the Outstanding Unvested PRSUs shall become payable in accordance with Section 3(c) and no Outstanding Unvested PRSUs shall convert into RSUs as described above, and (ii) if it is determined that the Performance Metrics for the Second Designated Period were not met, then all of such Outstanding Unvested PRSUs shall terminate and be forfeited as provided in Section 3(c) and no RSUs will be issued.

(d) None of the RSUs issued to Grantee in connection with a Change of Control pursuant to this Section 5 shall be immediately vested as of the date of such Change of Control (unless otherwise provided below). All of such RSUs shall vest on December 31, 2018 (for purposes of this Section 5, the “Vesting Date”), regardless of whether the Company has then achieved any of the Performance Metrics if the Grantee’s employment with the Company and its Affiliates continues through the period commencing on the date of the Change of Control and ending on the Vesting Date (the “Vesting Period”).

(e) If the Grantee’s employment with the Company and its Affiliates terminates during the Vesting Period, the right to the RSUs shall be as follows:

(i) If the Grantee’s employment with the Company or its Affiliates is terminated by the Company For Cause or the Grantee resigns without Good Reason, including by Retirement that is not an Approved Retirement or the Grantee’s voluntary departure, the RSUs will terminate immediately, no RSU Shares shall be issued to Grantee and all of the Grantee’s rights to the RSUs and the RSU Shares hereunder shall be forfeited.

(ii) If the Grantee’s employment with the Company or its Affiliates is terminated by the Company or an Affiliate other than For Cause, by the Grantee’s resignation for Good Reason or by reason of Grantee’s employer ceasing to be an Affiliate following a Change of Control at any time following the Change of Control, then all of the RSUs shall vest immediately, and the Grantee shall be entitled to receive all of the RSU Shares he would have been entitled to receive on the Vesting Date with respect thereto.

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(iii) If the Grantee dies or the Company or an Affiliate of the Company terminates Grantee’s employment due to Grantee’s long-term disability (within the meaning of Section 409A of the Code), then all of the RSUs shall vest and the Grantee shall be entitled to receive all of the RSU Shares with respect thereto. These Shares will be issued within sixty (60) days after the date of death or termination of employment.

(iv) In the event of Grantee’s Approved Retirement, then the number of RSUs that will vest and Shares issued in connection therewith shall be pro-rated downward based on the actual number of calendar days that elapsed from the date the Award was initially granted under this Agreement to the date of such Approved Retirement, versus the total number of calendar days from September 4, 2015 to December 31, 2018; provided, however, that no RSU Shares shall be issued and all of the Grantee’s rights to the RSUs and any Shares otherwise due shall be forfeited, expire and terminate unless (i) the Company shall have received a Release and Waiver (and said Release and Waiver shall have become irrevocable in accordance with its terms) prior to the 50th day following Grantee’s termination of employment and (ii) the Grantee shall have complied with the covenants set forth in Section 12 of this Agreement.

(v) In the event that, immediately following a Change of Control, a successor organization does not convert, replace or assume the RSUs, all of the RSUs shall immediately vest and the Grantee shall be entitled to receive all of the RSU Shares represented thereby.

(f) In all cases, any issuance of RSU Shares upon vesting of the RSUs in accordance with this Section 5 shall be made promptly and, in any event, within twenty (20) days following the date such RSUs shall become vested. For this purpose, RSUs vesting on account of (w) a termination by the Company other than For Cause, (x) resignation by the Grantee for Good Reason, (y) Grantee’s employer ceasing to be an Affiliate following a Change of Control at any time following the Change of Control, or (z) an Approved Retirement, shall be treated as vesting on the Company’s receipt of the required Release and Waiver but delivery of the RSU Shares at that time shall not obviate the need to comply with the covenants contained in Section 12 until the Covenant Termination Date (as defined in Section 12) in order to retain the RSU Shares then delivered.

(g) The Company (or any successor organization) may require the Grantee to enter into a restricted stock unit award agreement that replaces this Agreement and reflects the terms described above.

6. Settlement. The Final Award shall be settled by the issuance of Shares and not by payment of any cash, notwithstanding any provision of the 2013 EIP.

7. Withholding. Pursuant to the 2013 EIP, the Company shall have the right to require the recipient to remit to the Company an amount sufficient to satisfy federal, state, local or other withholding tax requirements if, when, and to the extent required by law (whether so required to secure for the Company an otherwise available tax deduction or otherwise) attributable to any Final Award awarded under this Agreement, including without limitation, the award or lapsing of stock restrictions on such Final Award. The obligations of the Company under this Agreement shall be conditional on satisfaction of all such withholding obligations and the Company shall, to the extent permitted by law, have the right to deduct any such taxes from any payment of any kind otherwise due

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to the Grantee. However, in such cases Grantee may elect, subject to any reasonable administrative procedures for timely compliance established by the Committee, to satisfy an applicable withholding requirement, in whole or in part, by having the Company withhold a portion of the Shares or RSU Shares to be issued under this Award to satisfy the Grantee’s tax obligations. The Grantee may only elect to have Shares or RSU Shares withheld having a Market Value on the date the tax is to be determined equal to the minimum statutory total withholding taxes arising upon the vesting of any Shares or RSU Shares. If the Grantee has not submitted an election on or before the thirtieth (30) day prior to the applicable Determination Date, Grantee shall be deemed to have elected to have shares withheld from the Shares or RSU Shares to be issued under this award to satisfy the Grantee’s tax obligation. All elections shall be irrevocable, made in writing, signed by the Grantee, and shall be subject to any restrictions or limitations that the Committee deems appropriate.

8. Other Provisions.

(a) This Agreement does not give the Grantee any right to continue to be employed by the Company or any of its Affiliates, or limit, in any way, the right of the Company or any of its Affiliates to terminate the Grantee’s employment, at any time, for any reason not specifically prohibited by law.

(b) The Company is not liable for the non-issuance or non-transfer, nor for any delay in the issuance or transfer of any Shares or RSU Shares due to the Grantee upon the applicable Settlement Date with respect to any Final Award which results from the inability of the Company to obtain, from each regulatory body having jurisdiction, all requisite authority to issue or transfer shares of common stock of the Company if counsel for the Company deems such authority necessary for the lawful issuance or transfer of any such Shares or RSU Shares. Acceptance of this Award constitutes the Grantee’s agreement that the Shares or RSU Shares subsequently acquired hereunder, if any, will not be sold or otherwise disposed of by the Grantee in violation of any applicable securities laws or regulations.

(c) The Final Award and entitlement to the Shares or RSU Shares are subject to this Agreement and Grantee’s acceptance hereof shall constitute the Grantee’s agreement to any administrative regulations of the Committee.

(d) All decisions of the Committee upon any questions arising under the 2013 EIP and LTI Plan or under these terms and conditions shall be conclusive and binding, including, without limitation, those decisions and determinations to adjust the Award made by the Committee pursuant to the authority granted under Section 8 of the 2013 EIP.

(e) No rights hereunder related to this Award or the Final Award shall be transferable, voluntarily or otherwise and no rights hereunder related to the underlying Target Shares or RSU Shares shall be transferable until such time, if ever, that the Shares or RSU Shares are earned and delivered.

9. Incorporation of 2013 EIP and LTI Plan Terms. This Award is granted subject to all of the applicable terms and provisions of the 2013 EIP and the LTI Plan, including without limitation, the provisions of Section 7.7(e) and Section 8 of the 2013 EIP. Capitalized terms used but not defined herein shall have the meaning assigned under the 2013 EIP and the LTI Plan. In the event of any conflict between the terms of this Agreement and the terms of the 2013 EIP and LTI Plan, the provisions of the 2013 EIP and LTI Plan shall control.

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10. Miscellaneous. This Agreement shall be construed and enforced in accordance with the laws of the State of Delaware, without regard to the conflict of laws principles thereof and shall be binding upon and inure to the benefit of any successor or assign of the Company and any executor, administrator, trustee, guardian, or other legal representative of the Grantee. This Agreement may be executed in one or more counterparts all of which together shall constitute one instrument.

11. Tax Consequences.

(a) The Company makes no representation or warranty as to the tax treatment of this Award or the Final Award, including upon the issuance of the Shares or RSU Shares or upon the Grantee’s sale or other disposition of the Shares or RSU Shares. The Grantee should rely on the Grantee’s own tax advisors for such advice. Notwithstanding the foregoing, the Grantee and the Company hereby acknowledge that both the Grantee and the Company may be subject to certain obligations for tax withholdings, social security taxes and other applicable taxes associated with the vesting of the PRSUs or the Shares by the Grantee pursuant to this Agreement. The Grantee hereby affirmatively consents to the transfer between his or her employer and the Company of any and all personal information necessary for the Company and his employer to comply with its obligations.

(b) All amounts earned and paid pursuant to this Agreement are intended to be paid in compliance with, or on a basis exempt from, Section 409A of the Code. This Agreement, and all terms and conditions used herein, shall be interpreted and construed consistent with that intent. However, the Company does not warrant all such payments will be exempt from, or paid in compliance with, Section 409A. The Grantee bears the entire risk of any adverse federal, state or local tax consequences and penalty taxes which may result from payments made on a basis contrary to the provisions of Section 409A or comparable provisions of any applicable state or local income tax laws.

12. Certain Remedies.

(a) If at any time prior to the last day of the two (2) year period after termination of the Grantee’s employment with the Company and its Affiliates (the “Covenant Termination Date”), any of the following occur:

(i) the Grantee unreasonably refuses to comply with lawful requests for cooperation made by the Company, its Board, or its Affiliates;

(ii) the Grantee accepts employment or a consulting or advisory engagement with (A) any Competitive Enterprise (as defined in Section 12(c)) of the Company or its Affiliates, or (B) any Significant Retailer (as defined in Section 12(d)), or the Grantee otherwise engages in competition with the Company or its Affiliates;

(iii) the Grantee acts against the interests of the Company and its Affiliates, including recruiting or employing, or encouraging or assisting the Grantee’s new employer to recruit or employ an employee of the Company or any Affiliate without the Company’s written consent;

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(iv) the Grantee fails to protect and safeguard while in the Grantee’s possession or control, or surrender to the Company upon termination of the Grantee’s employment with the Company or any Affiliate or such earlier time or times as the Company or its board of directors or any Affiliate may specify, all documents, records, tapes, disks and other media of every kind and description relating to the business, present or otherwise, of the Company and its Affiliates and any copies, in whole or in part thereof, whether or not prepared by the Grantee;

(v) the Grantee solicits or encourages any person or enterprise with which the Grantee has had business-related contact, who has been a customer of the Company or any of its Affiliates, to terminate its relationship with any of them;

(vi) the Grantee takes any action or makes any statement, written or oral, that disparages the business, products, services or management of Company or its Affiliates, or any of their respective directors, officers, agents, or employees, or the Grantee takes any action that is intended to, or that does in fact, damage the business or reputation of the Company or its Affiliates, or the personal or business reputations of any of their respective directors, officers, agents, or employees, or that interferes with, impairs or disrupts the normal operations of the Company or its Affiliates; or

(vii) the Grantee breaches any confidentiality obligations the Grantee has to the Company or an Affiliate, the Grantee fails to comply with the policies and procedures of the Company or its Affiliates for protecting confidential information, the Grantee uses confidential information of the Company or its Affiliates for his own benefit or gain, or the Grantee discloses or otherwise misuses confidential information or materials of the Company or its Affiliates (except as required by applicable law); then

(1) this Award shall terminate and be cancelled effective as of the date on which the Grantee entered into such activity, unless terminated or cancelled sooner by operation of another term or condition of this Agreement, the 2013 EIP or the LTI Plan;

(2) any Shares or RSU Shares acquired and held by the Grantee pursuant to the Award during the Applicable Period (as defined below) may be repurchased by the Company at a purchase price of $0.01 per share; and

(3) any after-tax proceeds realized by the Grantee from the sale of Shares or RSU Shares acquired through the Award during the Applicable Period shall be paid by the Grantee to the Company.

(b) The term “Applicable Period” shall mean the period commencing on the later of the date of this Agreement or the date which is one (1) year prior to the Grantee’s termination of employment with the Company or any Affiliate and ending on the Covenant Termination Date.

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(c) The term “Competitive Enterprise” shall mean a business enterprise that engages in, or owns or controls a significant interest in, any entity that engages in, the manufacture, sale or distribution of mattresses or pillows or other bedding products or other products competitive with the Company’s products. Competitive Enterprise shall include, but not be limited to, the entities set forth on Appendix B hereto, which may be amended by the Company from time to time upon notice to the Grantee. At any time the Grantee may request in writing that the Company make a determination whether a particular enterprise is a Competitive Enterprise. Such determination will be made within fourteen (14) days after the receipt of sufficient information from the Grantee about the enterprise, and the determination will be valid for a period of ninety (90) days commencing on the date of determination.

(d) The term “Significant Retailer” means those retailers identified in Appendix A under the heading “RETAILERS.” The Grantee acknowledges that the Significant Retailers may now or in the future compete directly or indirectly with the Company, and that, whether or not a Significant Retailer competes directly with the Company, the Grantee because of his knowledge of the industry and his knowledge of confidential information about the Company’s commercial relationships with many large retailers, including one or more of the Significant Retailers, could damage the Company’s competitive position and business if he worked with a Significant Retailer in any of the capacities described above.

13. Right of Set Off. By executing this Agreement, the Grantee consents to a deduction from any amounts the Company or any Affiliate owes the Grantee from time to time, to the extent of the amounts the Grantee owes the Company under Section 12 above, provided that this set-off right may not be applied against wages, salary or other amounts payable to the Grantee to the extent that the exercise of such set-off right would violate any applicable law. If the Company does not recover by means of set-off the full amount the Grantee owes the Company, calculated as set forth above, the Grantee agrees to pay immediately the unpaid balance to the Company upon the Company’s demand.

14. Nature of Remedies.

(a) The remedies set forth in Sections 12 and 13 above are in addition to any remedies available to the Company and its Affiliates in any non-competition, employment, confidentiality or other agreement, and all such rights are cumulative. The exercise of any rights hereunder or under any such other agreement shall not constitute an election of remedies.

(b) The Company shall be entitled to place a legend on any certificate evidencing any Shares acquired upon vesting of this Award referring to the repurchase right set forth in Section 12(a) above. The Company shall also be entitled to issue stop transfer instructions to the Company’s stock transfer agent in the event the Company believes that any event referred to in Section 12(a) has occurred or is reasonably likely to occur.

15. Clawback Policy. The Grantee acknowledges receipt of a copy of the Company’s Clawback Policy, and acknowledges and agrees that all Shares issued under this Agreement will be subject to the Clawback Policy or any amended version thereof and any other clawback policy adopted by the Board of Directors of the Company.

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In Witness Whereof, the parties have executed this 2015 Performance Restricted Stock Unit Award Agreement as a sealed instrument as of the date first above written.

[Signature Page to 2015 Performance Restricted Stock Unit Award Agreement]

Appendix A

PERFORMANCE METRICS FOR THE AWARD

DETERMINATION OF FINAL AWARDS

A. Target Based on Adjusted EBITDA. Subject to Section 4 of the Agreement, 100% of the Target Shares (620,000 Shares) shall vest if Adjusted EBITDA for the First Designated Period is greater than $650 million. Subject to Section 4 of the Agreement, 33% of the Target Shares (or 206,667 shares) shall vest if (i) no Target Shares vested for the First Designated Period and (ii) Adjusted EBITDA for the Second Designated Period is greater than $650 million.

B. Definitions and Method of Calculating Performance Metrics. The Final Award for the applicable Designated Period shall be determined pursuant to the following provisions and rules:

App. A

Appendix B

Competitive Enterprises of the Company and its Affiliates

App. B

RETAILERS

App. B